1 The nth term of a sequence is n 5 2

.

(a) Find the 6th term of this sequence [1]

(b) Find the greatest number in this sequence [1] , ,

3

G m n 5 4 2

Find the value of G when m = 6 and n = 15.

G = [1]

2 The stem-and-leaf diagram shows the age of each of 16 adults. 3 2 3 3 5 6 7 4 0 1 5 5 6 8 9 5 1 1 1

Key: 3 | 2 represents age 32 years

(a) Find the mode years [1]

(b) Find the median years [1]

(c) Find the percentage of the 16 adults with an age of less than 38 years % [2]

4 (a) The scale diagram shows the position of town A on a map.

Town B is 12 km from town A on a bearing of 080°.

Using a scale of 1 cm represents 2 km, mark the position of town B on the diagram. North A

Scale: 1 cm to 2 km

[2]

(b) The bearing of C from D is 130°.

Work out the bearing of D from C. [2]

5 (a) The diagram shows a regular decagon.

AB is a line of symmetry of the decagon. A B d ° NOT TO SCALE

Work out the value of d.

d = [3]

(b) The exterior angle of a regular polygon with n sides is 45°.

Work out the value of n.

n = [1] , ,

8 m is a positive integer.

Write these values in order of size, starting with the smallest. m 33% of m 3 1 of m 320% of m 10 , , , [2]

smallest 3 , ,

6 Simplify.

(a) y y 2 5

[1]

(b) x x 3 5 3 5

[2]

7 D E F y x – 6 – 7 – 8 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 7 8 9 10 11 12 13 14 15 – 3 – 2 – 1 1 2 3 4 5 6 7 8 9 10 11 12 0 – 4 – 5 – 6 – 7 – 8 6

(a) Describe fully the single transformation that maps triangle D onto triangle E [2]

(b) Describe fully the single transformation that maps triangle D onto triangle F [3] , ,

9 Draw a ring around the calculation that is equivalent to n 2 5 3 ' . n 2 3 5

n 3 5 1

n 5 13

n 1 5 13

n 1 13 5

[1] 10 Solve the simultaneous equations.

You must show all your working.

x y x y 3 5 5 2 5 45 +

=

x = y = [2]

11 .2 89 10 1

. 10 1 3 12

. 10 8 3 1

10 9 1 1

.2 10 03 5

.3 10 0 2

Use a number from the box to complete each statement.

The number that is not written in standard form is The largest number is The smallest number is [2] 12 A vase contains flowers that are red or pink or white.

Ruth picks a flower at random from the vase.

The probability that the flower is not red is 0.9 .

The probability that the flower is not pink is 0.65 .

Find the probability that the flower is white [2] 13 The point (5, 1024) lies on the curve y cx

, where c is a whole number.

Find the y-coordinate of the point on the curve with x-coordinate -2 [3] , ,

14 These expressions are all equal in value.

x 3 5 2

x 10- y 11 +

Find the value of y.

y = [5] 15 The population of a town is 54 000.

The population is decreasing exponentially at a rate of 2% per year.

(a) Calculate the decrease in the population at the end of 4 years [3]

(b) Find the number of complete years it takes for the population of 54 000 to first fall below 44 000 years [2] , ,

16 Expand and simplify.

(a) ( ) ( ) x x 7 2 4 3 5 + +

[2]

(b) ( )( ) x y x y 3 5 2

[2] 17 Make t the subject of the formula.

x t t 5 7

t = [3] , ,

18 102° 41.3 cm NOT TO SCALE 64.5 cm 70.2 cm 52.1 cm x° y°

(a) Calculate the value of x.

x = [3]

(b) Calculate the value of y.

y = [3] , ,

19

( )x 5 f x

( )x x 3 2 g

( )x x 1 h 2

(a) Find ( ) 5 f [1]

(b) Find ( )x 8 g [1]

(c) Find . ( )x g 1

( )x g 1

• [2]

(d) Find the positive solution of ( )x 364 gh

.

x = [3]

(e) Find .) 12 ( ff 1

[1]

20 y x x x 3 13 3 2

(a) Find x y d d [2]

(b) Find the gradient of the curve y x x x 3 13 3 2

• at the point where x 3 = [2] 21 A dressmaker takes 75 hours to make 31 dresses.

In week 1, she takes a total of 12 hours 30 minutes to make the first 4 dresses.

In week 2, she makes the remaining 27 dresses at a constant hourly rate.

Work out the percentage increase in her hourly rate of making dresses from week 1 to week 2 % [4]

22 (a) 45 mm x mm NOT TO SCALE 10 mm 14 mm

The diagram shows two mathematically similar triangles.

Find the value of x.

x = [2]

(b) The surface areas of two mathematically similar containers are 124 cm2 and 279 cm2.

The capacity of the smaller container is 56 ml.

Find the capacity of the larger container ml [3] , ,

23 The table shows some information about the mass of each of 200 oranges. Mass (m grams) m 2 0 180 0 1 G m 2 2 0 00 1 1 G m 21 2 0 15 1 G m 215 230 1 G Frequency 32 64 74 30

(a) Calculate an estimate of the mean mass of an orange g [4]

(b) Sarah draws a histogram to show this information.

The table shows the height of one of the bars for this histogram.

Complete the table. Mass (m grams) m 2 0 180 0 1 G m 2 2 0 00 1 1 G m 21 2 0 15 1 G m 215 230 1 G Height of bar (cm) 7.4

[3] , ,

24 13 cm 6.4 cm 5.1 cm NOT TO SCALE C D G H E F A B

The diagram shows a cuboid ABCDEFGH.

AE = 6.4 cm, EH = 5.1 cm and AG = 13 cm.

(a) Calculate EF.

EF = cm [3]

(b) Calculate the angle between the line AG and the base EFGH of the cuboid [3] , ,

25 Jenna has a length of wire measuring 68 cm, correct to the nearest cm.

From this wire she cuts off two smaller pieces • a piece of length 4.7 cm, correct to the nearest mm • a piece of length 10.0 cm, correct to the nearest mm.

Work out the lower bound and the upper bound for the length of the wire remaining.

Lower bound = cm

Upper bound = cm

[3] , ,

26 m p B C F D A E NOT TO SCALE

ABCD is a parallelogram.

m AB = and p AD = .

F is a point on BC and BF = 4FC.

E is a point on AD and AE : ED = 1 : 2.

(a) Find EF , in terms of m and p, in its simplest form [3]

(b) EF and DC are extended to meet at the point G.

Find CG, in terms of m and/or p, in its simplest form. [2] , ,